SAVINGS - INVESTMENTS Model In EGYPT

Cherine Mohamed Morsi

School of Computing, Engineering and Technology University of Sunderland

E-mail: shereen_morsi@hotmail.com

Professor Alfredo Moscardini

School of Computing, Engineering and Technology University of Sunderland

E-mail:alfredo.moscardini@sunderland.ac.uk

Abstract

The purpose of the System Dynamics method is to study the relationship between structure and behavior in non-linear, dynamic systems. In such systems, the significance of various structural components to the behavior pattern exhibited, changes as the behavior unfolds. Changes in structural significance, in turn modifies that behavior pattern, which, in turn, feeds back to change the relative significance of structural components. We develop a macroeconomic model which we can study the characteristics of this feedback between structure and behavior. This model is based on multiplier-accelerator model, and inventory – adjustment model. This work is an extension of the work by Nathan Forrester on the use of basic macroeconomic theory to stabilize policy analysis. Our main contribution, in this paper, is embedding the gap between savings and investments that already exist in Egyptian economy and how eliminating this gap. Explaining the reasons beyond this problem need first exhibit Egyptian economic cycle representing in production Cycle: that produce gross domestic production (GDP), The GDP depends on potential production (which consists of Labor force and capital that available in our society) and total demand in short-term. Capital Formation cycle: That depends on Total Domestic Investment (which consists of public investment (government sector) and private investment (business, household sector). The Total Domestic investment depends on what ‘s available from local resources (Government’s revenue and total local savings). The macroeconomic level contains many feedback loops that require from us to offer a structural interpretation of the behavior exist in Egyptian economy.

Introduction

Collecting savings and directing them to the various investment fields are the main requirements of development, therefore achieving increasing rates of economic development. This requires the presence of local savings sufficient to finance the investment necessary to achieve the required accumulation of capital to make the economics growth exceeds the population growth.

Thus we see a relationship between the savings and the economic growth, the more the savings, the more the investments and the higher the rate of growth of production through the accumulation of capital. This paper is trying to explain the previous savings – investments problem by using system dynamic approach that will help us evaluate the current problems and the proposed solution.

0

10000

20000

30000

40000

50000

60000

70000

80000

1992 1993 1994 1995 1996 1997 1998 1999 2000

Investments

Savings

Through the graph, it is obvious that investments is increasing more than the increase of local savings, this gap means there is a shortages in capital requirements to build internal production capacity to achieve economic growth and development. That creates a tendency to resort to internal and external sources of finance. One of the most important external sources is external debt. Managing internal and external debt represents a real challenge to the state. With the shortage of domestic Savings to feed the required growth, the dependency on internal and external capital flows, including debt, becomes a necessity. But the effects of the build up of debt have crucial negative effect on the recipient economy in the long run.

Guided by the economic models suggesting that growth rate can be stepped up by increasing Savings for Investment, the government has often resorted to local and foreign capital borrowing to supplement domestic savings in their efforts to fuel industrialization and production capacity. The borrowed capital is also often used to finance capital imports necessary to expand the export industries and for capital outlays for upgrading the infrastructure.

Conceptual Model

Dynamic Hypothesis

The inadequacy of domestic capital and savings leads to a shortage of satisfying domestic development and industrialization plans. In the beginning of the borrowing process, capital and investments increase significantly, levels of expected income and production increase and further development targets are set for the future, so local and foreign debt is required. The process is reinforcing and growing significantly .A buildup of internal capacity mean achieve desired capital may lead to the easiest way which is borrowing, but at a certain point of time the debt increase and we should pay it in maturity period. So to achieve high economic growth depend on the recourses that available to invest, but when trying to reach this highly growth by using debt it lead to decrease the income of our country to pay the loans by interest rate and the effect of it appear on low level of savings and this increase the gap between the savings and investment. Structural Assumptions:

To capture the process, we must start with describing the internal mechanisms of capacity buildup via capital acquisition, the domestic savings and the total domestic investments flows that lead to the aggregation of domestic income or production (GDP). This cycle can be describes with the multiplier accelerator mechanism first developed by Samuelson 1939.

The first important concept in the multiplier-accelerator model is the mutual dependency of consumption and output. Consumption depends on the level of output, and output responds to the level of aggregate demand. Together represent the multiplier process; it is positive loop feedback reinforcing process. Through the multiplier, a disturbance in demand produces a change in output and a proportional change in consumption, which feeds backs to further disturbance in aggregate demand.

The second important concept in the multiplier –accelerator model is that investment depends on demand. The model represents investment as a function of the change in consumption, but the underlying concept is that increased demand requires increased capital stock to maintain factor balance in the production process. For the purposes of this study it is convenient to restate the relationship by expressing desired investment as a function of desired capital and desired capital as a function of the expected long-term demand. This dependence of investment on demand creates the accelerator process. Through the accelerator, a disturbance in demand produces a change in output and a proportional change in desired capital and desired investment, which disturbs demand.

Here a minor modification was made to the model; investment is determined by a simple stock adjustment formula for capital. Total capital investment is the sum of capital depreciation plus the difference between desired and actual capital the actual capital stock is the accumulated difference between investments depreciation. Another alteration of the basic model is the introduction of the production capacity concept. In basic model, output is a one period lag of demand, regardless of the capacity to produce. The assumption is changed so that output is affected by potential output as well as demand. And potential output is formed as Cobb-Douglas function of two factors, Labor force and Capital. Both Labor and capital are adjusted in response

to change in expected demand. Expected demand is a moving average of current demand. Employment responds to short-term change in demand, while capital responds to long-term change in demand. The difference between output and potential output is explained by change in capacity utilization. Primarily through the use of over and under time.

These two modifications to the model developed by Samuelson has been suggested also by Nathan Forrester in his distinguished study of the stabilization of the US economy.

We will introduce some modification to the assumptions of Nathan Forrester as well. In his model, Forrester assumes that investment is determined by a simple stock adjustment formula for capital .We will distinguish between desired investment, which is the difference between desired and actual capital stock plus capital-depreciation. And actual investment, which depends on the adequacy of total domestic investment capabilities. The model developed by Nathan Forrester assumes the actual and desired investment are the same and the economy can automatically provide the amounts required of investment, which is not true in the real world and especially in the case of Egypt. For the purpose of this study we will cut the major loop of the multiplier-accelerator model. Actual investment will be total domestic investment capacity and its depends on private investment (come from local savings in banks and it depends in fraction of investment for private sector) and public investment (come from government sector and it depends on current revenue for government and fraction of investment) Plus we will add foreign investment as fraction of GDP. The discrepancy between actual and desired investment will represent the desired loan. This paper will use the multiplier –accelerator model as a basic structure that show the accumulation of capital need desired investment and according to shortage resource lead government to finance by external debt and that will lead to accumulate loans and it will decrease through the loan payment which take from total income of the country.

None of the above modifications change the theory underlying the models of Samuelson or Nathan Forrester. They make more explicit the disequilabrium adjustment process that produce the mechanism of building up capital and output in response to change in demand and vise versa. These modifications serve the purpose of this study. The Second important concept is the Inventory –adjustment model, inventory is treated as the stock of finished goods, which increase by output and decrease by final sales, and inventory feedback to output through desired inventory investment by expected demand, desired inventory investment is equal the difference between desired and actual inventory, and desired inventory is proportional to long-term expected demand. The inventory loop adds to model to express about business cycle and determine the total aggregate demand in Egyptian economy.

Causal Loop Diagram

Investment

SavingsConsumption

DomesticInvestment

PotentialProduction

Capital

Desired Loan

PermanentIncome

CurrentDisposableincome

GovernmentSpending

Final Sales

Debt

+

+

+

+

-

+

+

+

-

+

+

+

+

+

CapitalDepreciation

+

AggregateDemand

+

+

-

DesiredInvestment

DesiredCapital

+

ForiegnInvestment

Production

+

+

Short-turmDemand

+

DesiredEmployment

+

Employment

+

+

GovernmentTransfer

+

DebtPayment

+

-

-

B1

Long-termDemand

DesiredInventory

+

+

DesiredInventoryInvestment

+

Inventory

+

-

+

+

B2

-

+

B3+

+

R1+

+

R2+

+

+

+

+

+

+

+

+

+

R3+

Danger Loop (R1): This loop start when the gap between total domestic investment desired investment created, the government tends to borrow as a way for increasing resources to achieve wanted investment and this will return achieving high economic growth, the debt will increase and will decreases by loan payment which lead to decrease permanent income, so the savings will decrease and it will lead to another loop of borrowing. Multiplier Process (R2):

In this loop consumption depend on the level of production, and production respond to the level of short term expected demand, when production increase, the current disposable income, and permanent income will increase so that will increase the level of consumption which makes increase in demand and lead to produce more and so on. Accelerator Process (R3): The investment depend on long term expected demand, when investment increase the capital, potential production, production, current disposable income and permanent income will increase which lead consumption to increase aggregate demand and that will raise long term expected demand and sequentially raise desired capital and desired investment. Business Cycle (B3): The effect s of this loop can be traced starting at aggregate demand, An increase in aggregate demand raises short term expected demand, which pushes up desired employment .The increase in desired employment raises employment and that will lead to greater production and accumulation of inventory so high level of inventory will decrease level of desired inventory investment.

FORMAL MODEL

Stock and Flow diagram

Capital Formation

Aggregate_Demand

Capital_Depreciation

Change_in_long_term

Total_Domestic_investment

Desired_Investment

Desired_loan

Money_Borrowed

Desiredt_Capital

Capital_investment

Time_to_adjust_long_term

Time_to_Adjust_Capital

Long_term_expected_demand

Average_life_of_Capital

Real_Interest_rate

Capital

Exponent_on_Capital

Demand For Production

Capital_to_Equilibruim_Capital

Short_term_expected_demand

Change_in_Employment

Desired_Employment

Change_in_short_term

Output_GDP

Time_to_adjust_short_term

Flexibility_of_Capacity_Utilization

Potential_output

Aggregate_Demand

Short_term_expected_demand

Capital

Equilibruim_Capital

Exponent_on_Capital

Short_term_expected_demand

Equilibruim_Production

Wages

Equilibruim_Employment

Employment

Time_to_adjust_employment

Inventory Adjustment

Aggregate_Demand

Capital_investment

Desired_Inventory

Final_Sales

Desired_inventory_investment

Final_SalesOutput_GDP

Consumption

Normal_inventory_Coverage Short_term_expected_demand

Gov_SpendingTime_to_adjust_inventory

Inventory

Income Creation

Output_GDP Tax_Revenue

Consumption

Current_Disposable_Income

Perceived_Debt

Change_in_permenant_income

Margin_propenstiy_to_consume

Permenant_Income

Time_to_smooth_income

Gov_Transfer

Debt formation

Interest_rate

Production

Desired_loan

Money_Borrowed

Total_Debt

Time_to_acquire_loans

Perceived_Payment

Lending_rate

Maturity_period

Loan_Payment

Percentage_of_debt_to_production

Effect_of_Debt_to_Production_on_Desired_loan

Saving sector

Permenant_Income

Average_proponsity_to_saveTotal_Domestic_investment

Saving_rate

Average_propensity_to_consume

Total_Savings

Foriegn_Investment

Investment_fraction

Investment_from_Savings

Documentation

The following are the model variables with full description. Appendix (1) contains powersim printout of all variables, equations and documentation sorted alphabetically Production (GDP) : Production is a weighted average of potential production and short-term expected demand.

LE means Local Pounds • Production measured in (LE/Year) • Potential production measured in (LE/Year) • Short-term expected demand measured in (LE/Year) • Flexibility of capacity utilization measured in (Dimensionless)

Potential production: Potential production is determined by labor force (represent in no. of employees) and capital stock according to Cobb-Douglas production function.

• Equilibrium production measured in (LE/Year) • Employment to Equilibrium Employment measured in (persons)

Production = Potential_Production*(1-Flexibility_of_Capacity_Utilization) + Short_term_expected_demand * Flexibility_of_Capacity_Utilization

Potential production= Equilibruim_Production*(Employment_to_Equilemployment)^ (1-Exponent_on_Capital) * (Capital_to_Equilibruim_Capital)^Exponent_on_Capital

• Capital to Equilibrium capital measured in (LE) • Exponent on capital measured in (Dimensionless)

Employment: Employment is the total man-hours dedicated to production.

• Employment measured in (persons)

Change In Employment:

The Change in Employment determined by the net difference between Desired and actual Employment and divide by time to adjust employment.

• Change in employment measured in (Persons/Year) • Desired employment measured in (persons) • Time to adjust employment measured in (years)

Desired Employment: Desired employment is proportional to short-term expected demand. It’s equal to exponent on labor in the production function multiplied by short-term expected demand divided by the wages.

• Desired employment measured in (Persons) • Short-term expected demand measured in (LE/Year) • Wages measured in (LE/persons/year)

Short-term expected demand: Sectors that produce have their expectation about sales in future ,so short-term expected demand determined as average of aggregate demand .

• Short-term expected demand (LE/Year)

Change In shot-term expected demand :

The Change in short-term expected demand determined by the net difference between aggregate demand and short-term expected demand and divide by time to adjust short-term expected demand.

• Change short-term expected demand measured in ((LE/Year/Year) • Aggregate demand measured in (LE/Year) • Time to adjust short-term expected demand measured in (Years)

Change in employment = (Desired_Employment - Employment) /Time_to_adjust_employment

Desired employment = (1- exponent on capital)* short-term expected demand / wages

Change short-term expected demand = (Aggregate demand – short-term expected demand)/ time to adjust short-term expected demand

Capital:

The Stock of Capital is accumulated by investment and decreased by deprecation. Therefore, the rate of change in capital is equal to the difference between Capital investment and Capital depreciation.

• Capital measured in (LE)

Capital investments: The Capital investment is the total investments that lead to increase the capital, and it is summation of available of the total domestic investments and the money borrowed.

• Capital investments measured in (LE/Year) • Money Borrowed measured in (LE/Year) • Total Domestic investments measured in (LE/Year)

Capital Depreciation: Physical capital is assumed to have a constant average service life. Capital depreciation is there for proportional to capital stock.

• Capital Depreciation measured in (LE/Year) Desired Investment: The desired investments is determined by the difference between desired capital which the county need to reach it to achieve highly economic growth and capital divide by the time need to achieve this capital plus capital depreciation.

• Desired investment measured in (LE/Year) • Desired Capital measured in (LE) • Time to adjust capital measured in (Years)

Desired Capital: Capital unlike labor is a long-lived asset for production sector. Capital should respond more slowly than labor to changes in demand and inventory conditions. Desired capital is therefore a function of long term expected demand.

• Desired capital measured in (LE/Year) • Long term expected demand measured in (LE) • Interest rate measured in (fraction/Year) • Average life of capital measured in (years)

Capital investments = MAX(0,(Total_Domestic_investment + Money_Borrowed))

Capital Depreciation = Capital / Average Life of Capital

Desired investments = ((Desired Capital - Capital) + Capital Depreciation) / Time to adjust Capital

Desired capital = Exponent on capital *Long term expected demand /(1/average life of capital)+ interest rate

Long term expected demand The long term expected demand is an exponential average of aggregate demand , and it consider expectation of long term demand, and it initialize by equal the total production (GDP).

• Long term expected demand measured in (LE).

Change in Long-term expected demand: The Change in Long-term expected demand determined by the net difference between aggregate demand and Long-term expected demand and divide by time to adjust Long-term expected demand.

• Change long-term expected demand measured in ((LE/Year/Year) • Aggregate demand measured in (LE/Year) • Time to adjust long-term expected demand measured in (Years)

Inventory: The rate of change in inventory is the difference between production and final sales.

• Inventory measured in (LE)

Final Sales: The final sales represent the total demand in economy, so it’s the summation of consumption plus investment and government expenditure.

• Final sales measured in (LE/Year) • Consumption measured in (LE/Year) • Capital investment measured in (LE/Year) • Government expenditure measured in (LE/Year)

Desired inventory: Desired inventory is assumed to be proportional to short-term expected demand.

• Desired inventory measured in (LE) • Normal inventory coverage measured in (Years) Desired inventory investment: The desired inventory investment is determined by the difference between desired and actual inventory. • Desired inventory investment measured in (LE/Year)

Final Sales = consumption + capital investments + government expenditure

Change Long-term expected demand = (Aggregate demand – Long-term expected demand)/ time to adjust long-term expected demand

Desired inventory = Normal inventory coverage * short-term expected demand

Desired inventory investment = (desired inventory – inventory) / time to adjust inventory

• Desired inventory measured in (LE) • Inventory measured in (LE) • Time to adjust inventory measured in (Years) Permanent income: Permanent income is average of current disposable income , the rate of change in permanent income is the fraction of the discrepancy between current disposable income and permanent income . • Permanent income measured in (LE/Year)

Change in permanent income : The change in permanent income is the difference between current disposable income, permanent income and perceived debt service.

• Change in Permanent income measured in (LE/Year/Year) • Current disposable income measured in (LE/Year) • Perceived debit service measured in (LE/Year) • Time to smooth income (Year)

Consumption:

The consumption is the amount of money spend on domestic products and services per year.

• Consumption measured in (LE/Year)

Total Savings:

Total Savings are the total deposits that exist in Banks from Government sector plus Non-Government sector and it is increased by saving rate and decreased by private investments.

• Total Savings measured in (LE)

Saving rate:

The saving rate is the rest of income that not consume and it depends on average propensity to save and permanent income

• Saving rate measured in (LE/Year) • Average propensity to save measured (fraction/year)

Saving rate =Permanent income *Average propensity to save

Change in permanent income=(Current disposable income-permanent income-perceived debit service)/ time to smooth income.

Consumption = Permanent income * Average Propensity to consume

Investment from Savings: The investment from savings means the resources that available from internal country and directed to invest in all projects .

• Investment from savings measured in (LE/Year)

Total Domestic investments The total domestic investments determined by total investment from government sector and non-government sector plus foreign investment .

• Total Domestic investments measured in (LE/Year)

Investment fraction:

The investment fraction is determined as percentage of local resources available. And it put as constant depend on the actual situation in country.

Tax Revenue:

The tax revenue is the total amount of money gained by the government from taxes per each year; it is defined by total GDP multiplied by the tax fraction.

• Tax Revenue measured in (LE/Year)

Total Debt: The total debt is considered the outstanding of loans and it accumulated by both money borrowed and accrual of interest rate and depleted by debt service rate.

• Total debt measured in (Units) Money Borrowed The money borrowed is consider the gap between desired investment and domestic investment , and the size of this gap determine the loan that will take from abroad. and time taking to get this loan .

• Rate of money borrowed measured in (Units/Year) • Gap (LE/Year) • Time to acquire loans (Years)

Investment from savings = Dleaymtr(otal_Local_Saving,1,1,Total_Local_Saving)*Invest_frac

Total Domestic investments = Investment_from_Savings + Foriegn_Investment

Tax Revenue = Production * TaxFraction

Money borrowed = MAX (0,Desired_loan/Time_to_acquire_loans) * Effect_of_Debt_Output_on_Desired_Loan

Desired Loan: The desired loan initialize when there is a difference between desired investment and total domestic investment and this difference lead to borrow local or foreign loan.

Loan Payment: The loan payment is the acquired loan according to maturity date.

• Loan payment measured in (Units/Year)

Perceived Payments: The payments are depend on the rate of money borrowed, lending rate of this loan, and how many years loan will stay until become acquired to pay.

• Payments measured in (Units/Year)

Lending rate: The lending rate is interest rate that should pay over the loan in the end of maturity date of loan. And the rate of lend is average by 7% annually. Interest Rate: This interest rate is determined by debt and lending rate; after it calculated it add to stock of total debt.

• Interest rate measured in (Units/Year)

Foreign investment:

The foreign investment is the total amount that foreign companies invest it in Egypt. And it will be one of alternative policies. Effect of total debt to production to acquire another loan: The effect of total debt to production to acquire loans means ,it represents state of the country by the ratio of total debt to production ,if this percentage high ,the country has to stop financing capital stock by borrowing money ,because the main problem in debt payment .

Desired Loan = MAX(Desired_Investment-Total_Domestic_investment,0)

Loan payment = Total_Debt / Maturity_period

Perceived Payment = (DELAYPPLINF(Loan_Payment,4,5))

Interest Rate = Total Debt * Lending rate

GRAPH(Percentage_of_debt_to_production,0,0.1,[1,0.93,0.85,0.74,0.66,0.57,0.53,0.46,0.4,0.33,0.26,0.2,0.17,0.13"Min:0;Max:1"])

Model Behavior

In this part we will try to describe the major phases of behavior of the model in the base run. and then describe the simulation results for two alternative policies and compare the results. 1-Analysis of the Base Run: The model in the base run is simulated a period of 50 years, and there are two main phases of behavior that we will discuss in detail.

Years

Saving_rate1

Capital_investment2

0 10 20 30 40 50

15,000

20,000

1

2

1

2

1

2

1

2

1

2

1

2

Years

Desired_Investment1

Total_Domestic_investment2

0 10 20 30 40 50

15,000

20,000

1

2

1

2

1

2

1

2

1

2

1

2

Years

Perceived_Payment1

Money_Borrowed2

0 10 20 30 40 500

3,000

6,000

1

21

2

1 21

2

1

2

1

2

Years

Production1

Aggregate_Demand2

0 10 20 30 40 50

95,000

100,000

105,000

110,000

115,000

120,000

1

2

1

2

12

12

1 21

Years

Capital_Depreciation1

Capital_investment2

0 10 20 30 40 50

14,000

16,000

18,000

20,000

22,000

1

2

1

2

1

2 1

21

2 1

The simulation shows significant oscillation in most variables .All variables share the same length of cycle period. In general we can say that in the high part of the cycle the dominant loops are the multiplier, accelerator loops, while in downward part of each cycle the dominant loops are representing in financing gap and debt payment. These oscillations indicate the effect of the existence of negative feedback loops and delays. The general behavior of the system can described from economic point as follows: There is a planned desired investment according a high total demand, but Total domestic investments are not covering it, due to the saving rate is less than the investment rate. The gap between total domestic investments and desired investments will be overcome by borrowing money to build production capacity, when desired loan acquire, investment in new capital stock increase and it required increase labor force and that lead to increase production capacity and current disposable income which affect on saving rate by increasing it, but the saving rate rise depends on average propensity to save and this average needs to increase first. The production rise will lead to increase consumption, so the total demand will increase which will lead to another cycle another, and the gap between saving and investment already exist ,so the country will borrow again ,but the outstanding of total debt grows significantly and debt payment is higher than loan acquisition rate .this mean the percentage of total debt to production is high. This high percentage will lead to decreasing money borrowed .The effect of it lead to capital investment starts fall below capital depreciation and according to it capital stock starts to fall.

If we simulate for more than 50 years, the results will be oscillations every 10 years but at lower levels, because the economy is trapped in loans that on the long run will highly decrease the levels of demand, production, and income.

Appendices

init Capital = 258000 flow Capital = -dt*Capital_Depreciation +dt*Capital_investment doc Capital = The Stock of Capital is acumaleted by capital investment and decreased by capital deprication , Therefore the rate of change in capital is equal to the difference between its. init Employment = 10 flow Employment = +dt*Change_in_Employment doc Employment = The Employment is defined as total employees are share in production. init Inventory = 30000 flow Inventory = +dt*Production -dt*Final_Sales init Long_term_expected_demand = 100000 flow Long_term_expected_demand = +dt*Change_in_long_term init Permenant_Income = 80000 flow Permenant_Income = +dt*Change_in_permenant_income doc Permenant_Income = Permanent income is an exponential average of current disposable income. init Short_term_expected_demand = 100000 flow Short_term_expected_demand = +dt*Change_in_short_term doc Short_term_expected_demand = The Short term expected demand is an exponential average of aggregate demand init Total_Debt = 0 flow Total_Debt = +dt*Interest_rate -dt*Loan_Payment +dt*Money_Borrowed init Total_Savings = 17000 flow Total_Savings = -dt*Investment_from_Savings +dt*Saving_rate doc Total_Savings = it is the total saving from government sector that exist in central bank aux Capital_Depreciation = Capital/Average_life_of_Capital doc Capital_Depreciation = Physical capital is assumed to have a constant average service life . Capital Depreciation is there for proportional to capital stock. aux Capital_investment = MAX(0,(Total_Domestic_investment+Money_Borrowed)) doc Capital_investment = It is the total investment that lead to increase the capital , and it is summtion of avaliable real total domestic investment . aux Change_in_Employment=(Desired_Employment-employment)/Time_to_adjust_employment doc Change_in_Employment = The change in Employment is equal the discrepancy between desired employment and actual employment divided by time to adjust employment. aux Change_in_long_term=(Aggregate_Demand-Long_term_expected_demand) /Time_to_adjust_long_term aux Change_in_permenant_income = (Current_Disposable_Income-Permenant_Income-Perceived_Payment)/Time_to_smooth_income aux Change_in_short_term = (Aggregate_Demand -Short_term_expected_demand)/Time_to_adjust_short_term doc Change_in_short_term = The change in short term is the difference between current aggregate demand and expected demand divided by time to adjust short term demand. aux Final_Sales = Capital_investment+Consumption+Government_Expenditure doc Final_Sales = it is the sum of consumption , investment and government expenditure . aux Interest_rate = Total_Debt*Lending_rate

aux Investment_from_Savings = Total_Savings*Investment_fraction aux Loan_Payment = Total_Debt/Maturity_period aux Money_Borrowed=MAX(0,Desired_loan/Time_to_acquire_loans)*Effect_of_Debt_to_Production_on_Desired_loan aux Production=Potential_Production*(1-Flexibility_of_Capacity_Utilization) + Short_term_expected_demand * Flexibility_of_Capacity_Utilization doc Production = Production is a weighted average of potential output and short term expected demand , And the weighting parameter is the flexibility of capacity utilization . aux Saving_rate = MAX(0,Permenant_Income*Average_proponsity_to_save) doc Saving_rate = The govenmnet saving rate is the annual saving from govrnment sector aux Aggregate_Demand = Final_Sales+Desired_inventory_investment aux Average_proponsity_to_save = (1-Average_propensity_to_consume) aux Capital_to_Equilibruim_Capital = Capital/Equilibruim_Capital aux Consumption = Permenant_Income*Average_propensity_to_consume doc Consumption = The consumption function is based on the permenant income hypothesis of Fredman . Consumption is equal to a constant fraction of permenant income, the constant of disposable income spent on consumption goods equals the average proponsity to consume. aux Current_Disposable_Income = Production-(Tax_Revenue-Gov_Insurance) doc Current_Disposable_Income = Current disposable income is defined as total output less net taxes aux Desired_Employment=((1-Exponent_on_Capital)*Short_term_expected_demand)/Wages aux Desired_Inventory = Normal_inventory_Coverage*Short_term_expected_demand aux Desired_inventory_investment=(Desired_Inventory-Inventory)/Time_to_adjust_inventory aux Desired_Investment=Capital_Depreciation+(Desiredt_Capital-Capital)/Time_to_Adjust_Capital doc Desired_Investment = Fixed Capital investment is given by a simple stock adjustment formula . the base rate of investment is equal to physical capital depreciation .The base rateis modified by the need to expand or contract the capital stock . desired investment is therefore equal to capital depreciation plus a fraction of the discrepancy between desired capital and actual capital stock and divided by time to adjust capital . aux Desired_loan = MAX(Desired_Investment-Total_Domestic_investment,0) aux Desiredt_Capital= Exponent_on_Capital * Long_term_expected_demand /(1/Average_life_of_Capital +Real_Interest_rate) doc Desiredt_Capital = Capital is a long lived asset for the production sector . And desired capital is therefore a function of long term expected demand . aux Effect_of_Debt_to_Production_on_Desired_loan=GRAPH(Percentage_of_debt_to_production,0,0.1,[1,0.93,0.85,0.74,0.66,0.57,0.53,0.46,0.4,0.33,0.26,0.2,0.17,0.13"Min:0;Max:1"]) doc Effect_of_Debt_to_Production_on_Desired_loan = it represent state of the country by the ratio of total debt to production . aux Employment_to_Equilemployment = Employment/Equilibruim_Employment aux Gov_investment = Tax_Revenue*Gov_investment_frac aux Gov_Saving = Tax_Revenue-(Current_gov_expenditure) aux Non_gov = Saving_rate-Gov_Saving aux Perceived_Payment = DELAYPPLINF(Loan_Payment,1,5)

aux Percentage_of_debt_to_production = Total_Debt/Production aux Potential_Production= Equilibruim_Production*(Employment_to_Equilemployment)^(1-Exponent_on_Capital)*(Capital_to_Equilibruim_Capital)^Exponent_on_Capital doc Potential_Production = Potential output is determine by the stock of capital and employment as cobb - Douglas production function. aux Tax_Revenue = (Production*Tax_rate) aux Total_Domestic_investment = Investment_from_Savings+Foriegn_Investment doc Total_Domestic_investment = The total domestic investment determined by govrnment investment and private investment plus foriegn investment const Average_life_of_Capital = 15 doc Average_life_of_Capital = A simple time constant for the exponential decay formula . The average life of capital will be set to the value of 15 years. A lot of empirical studies suggest the same value . const Average_propensity_to_consume = .83 doc Average_propensity_to_consume = The portion of income that is directed to consumption rater than savings and investment is relatively high const Current_gov_expenditure = 26211.4 doc Current_gov_expenditure = Government Expenditure consider the total amount that the government spend on paying (salaries or wages, pensions, commodity and service requirement, defense outlays, subsidies, social funds and others) . Government expenditure put as constant and increased annually by 10% as analysis of historical data. const Equilibruim_Capital = 258000 const Equilibruim_Employment = 10 const Equilibruim_Production = 100000 const Exponent_on_Capital = .25 const Flexibility_of_Capacity_Utilization = .5 doc Flexibility_of_Capacity_Utilization = it controls the under overutilization of plant and undertime and overtime for labor . it is supposed to vary between 0 and 1 the parameter is set her to .5 representing the case of egypt with little flexibility of capacity utilization due to the inadequacy of resources. const Foriegn_Investment = 1000 const Gov_Insurance = 10000 const Gov_investment_frac = .15 const Government_Expenditure = 20000 const Investment_fraction = .65 const Lending_rate = .07 const Maturity_period = 5 const Normal_inventory_Coverage = .30 const Real_Interest_rate = .03 const Tax_rate = .30 const Time_to_acquire_loans = 1 const Time_to_Adjust_Capital = 3 doc Time_to_Adjust_Capital = It represents the entire delay between the recognition of a change in capital needs and actual capital stock. the adjustment time reflects planning and delivery delays plus purposeful smoothing of investment activity. const Time_to_adjust_employment = .5

const Time_to_adjust_inventory = .5 const Time_to_adjust_long_term = 3 doc Time_to_adjust_long_term = it insulates capital investment from short run swings in demand Becasue capital has a long life , it should be adjusted only to relatively long run changes in demand . the smoothing time should be long enough to filter out most business cycle flctuations. const Time_to_adjust_short_term = .5 doc Time_to_adjust_short_term = it must be long enough to smooth out minor shifts in demand but short to permit recognition of business cycle variations in demand . The smoothing time must be approximately one year or less to track business cycle fluctuations. const Time_to_smooth_income = 2.5 doc Time_to_smooth_income = Milton Friedman, in his theory about consumption function, estimates the time to smooth permanent income to be 2.5 years. const Wages = 7500